The escape dynamics of passive Brownian particles from various type of confinements and opening structures has been extensively investigated in the recent literature [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. Usually, the exit rate from smoothly corrugated channel compartments is studied under the premises of Fick-Jacobs scheme[1]}, [5]}, [6]}, [7]}. An alternative method based on random walker schemes emerged very effective to handle cases for both smoothly as well as sharply corrugated walls [2]}, [10]}. However, both of these schemes lose their validity in case of persistent Brownian motion due to inertia or self-propulsion [3]}, [22]}, [23]}, [24]}.
